If 1, log _{10}left(4^{x}-2right) and log _{1 | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$2 \log _{10}\left(4^{ x }-2\right)=1+\log _{10}\left(4^{ x }+\frac{18}{5}\right)$

$\left(4^{ x }-2\right)^{2}=10\left(4^{ x }+\frac{18}{5}\right)$

Vedclass · Accepted Answer

$2$

Vedclass · Answer

$2 \log _{10}\left(4^{ x }-2ight)=1+\log _{10}\left(4^{ x }+\frac{18}{5}ight)$

$\left(4^{ x }-2ight)^{2}=10\left(4^{ x }+\frac{18}{5}ight)$

$\left(4^{ x }ight)^{2}+4-4\left(4^{ x }ight)-32=0$

$\left(4^{ x }-16ight)\left(4^{ x }+2ight)=0$

$4^{ x }=16$

$x =2$

$\left|\begin{array}{lll}3 & 1 & 4 \ 1 & 0 & 2 \ 2 & 1 & 0\end{array}ight|=3(-2)-1(0-4)+4(1)$

$=-6+4+4=2$

Similar Questions

If the sum of first $p$ terms of an $A.P.$ is equal to the sum of the first $q$ terms, then find the sum of the first $(p+q)$ terms.

Let $a _1, a _2, \ldots, a _{2024}$ be an Arithmetic Progression such that $a _1+\left( a _5+ a _{10}+ a _{15}+\ldots+ a _{2020}\right)+ a _{2024}= 2233$. Then $a_1+a_2+a_3+\ldots+a_{2024}$ is equal to ________

Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic progression. If $S_{3 n}=3 S_{2 n}$, then the value of $\frac{S_{4 n}}{S_{2 n}}$ is:

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day, $4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

If $a$ and $b$ are the roots of $x^{2}-3 x+p=0$ and $c, d$ are roots of $x^{2}-12 x+q=0$ where $a, b, c, d$ form a $G.P.$ Prove that $(q+p):(q-p)=17: 15$